Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
406 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C5×#1567 | C2 | semidirect |
| 4. #10601302 | C2 | semidirect |
| 5. #10600531 | C2 | semidirect |
| 7. #10598202 | C2 | semidirect |
| 70. #1567 | D5 | semidirect |
| 334. C5 | #10461 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10610790 | 2 |
| C5×#1567 | 2 |
| #10601320 | 2 |
| #10601302 | 2 |
| #10600531 | 2 |
| C2×#64679 | 2 |
| #10598202 | 2 |
| #10461 | 5 |